Journal of Algorithms - Analysis of algorithms
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We consider sums of functions of subtrees of a random binary search tree and obtain general laws of large numbers and central limit theorems. These sums correspond to random recurrences of the quicksort type, $X_n {\stackrel{\cal L}{=}} X_{I_n} + X'_{n-1-I_n} + Y_n$, $n \ge 1$, where In is uniformly distributed on {0,1,. . ., n-1 }, Yn is a given random variable, $X_k {\stackrel{\cal L}{=}} X'_k$ for all k, and, given In, XIn and X'n-1-In are independent. Conditions are derived such that $(X_n - \mu n )/\sigma \sqrt{n} {\stackrel{\cal L}{\rightarrow}} {\cal N}(0,1)$, the normal distribution, for some finite constants $\mu$ and $\sigma$.